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measures of center and dispersion

Course Code
Damian Dupuy

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Statistics Lecture
September 28, 2011
Statistics and Parameters
Graphs are limited in what they can tell us
Difficulty in making inferences about a population when looking
at a subset or sample
So we need to use numerical measures
Measures associated with a sample are called statistics
Parameter [population] and statistics [sample]
Measures of the Centre
oMost common measure of central tendency
oIt is the sum of all values divided by the number of
oSample measurement:
Median: value occupying the ‘middle position’ of an ordered set
of observations
oOrder of the observations, lowest to highest and find the
middle position
oUneven observations: odd number of observations
oEven observations: use the same formula but you’ll have
the add the two and divide it by two
Mode: value that occurs at the highest frequency
oAllows you to locate the peak of a relative frequency
Choosing an appropriate measure
Mean is usually the best but it is not the best when the
distribution is bi-modal and is not good with outliers which skew
the distribution
Measures of Dispersion
Range: simplest measure
oTakes difference between smallest and largest value in the
oIs influenced by outliers
oRange= Xmax- Xmin
Standard Deviation: comparing each value to the mean
Variance: always represented as S2, n-1 is because you are using
a sample
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